2,116 research outputs found
Numerical Integration of Nonlinear Wave Equations for General Relativity
A second-order numerical implementation is given for recently derived
nonlinear wave equations for general relativity. The Gowdy T cosmology is
used as a test bed for studying the accuracy and convergence of simulations of
one-dimensional nonlinear waves. The complete freedom in space-time slicing in
the present formulation is exploited to compute in the Gowdy line-element.
Second-order convergence is found by direct comparison of the results with
either analytical solutions for polarized waves, or solutions obtained from
Gowdy's reduced wave equations for the more general unpolarized waves. Some
directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps
Comparison of different objective functions for parameterization of simple respiration models
The eddy covariance measurements of carbon dioxide fluxes collected around the world offer a rich source for detailed data analysis. Simple, aggregated models are attractive tools for gap filling, budget calculation, and upscaling in space and time. Key in the application of these models is their parameterization and a robust estimate of the uncertainty and reliability of their predictions. In this study we compared the use of ordinary least squares (OLS) and weighted absolute deviations (WAD, which is the objective function yielding maximum likelihood parameter estimates with a double exponential error distribution) as objective functions within the annual parameterization of two respiration models: the Q10 model and the Lloyd and Taylor model. We introduce a new parameterization method based on two nonparametric tests in which model deviation (Wilcoxon test) and residual trend analyses (Spearman test) are combined. A data set of 9 years of flux measurements was used for this study. The analysis showed that the choice of the objective function is crucial, resulting in differences in the estimated annual respiration budget of up to 40%. The objective function should be tested thoroughly to determine whether it is appropriate for the application for which the model will be used. If simple models are used to estimate a respiration budget, a trend test is essential to achieve unbiased estimates over the year. The analyses also showed that the parameters of the Lloyd and Taylor model are highly correlated and difficult to determine precisely, thereby limiting the physiological interpretability of the parameter
Deleuze en het Zijn
In âDeleuze en het Zijnâ, David van Putten argues that despite the fact
that Deleuze barely discusses Heidegger in his Difference and Repetition, he
ultimately addresses the same philosophical problem as Heidegger. Both
Deleuze and Heidegger try to get away from the Aristotelian system of species
and genera because it does not do justice to reality. Van Putten argues
that the point where they depart from each other is how to approach this
problem: Deleuze disagrees with Heideggerâs decision to approach it only
from the question of Bein
Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial
(Short abstract). In Galilean physics, the universality of free fall implies
an inertial frame, which in turns implies that the mass m of the falling body
is omitted. Otherwise, an additional acceleration proportional to m/M would
rise either for an observer at the centre of mass of the system, or for an
observer at a fixed distance from the centre of mass of M. These elementary,
but overlooked, considerations fully respect the equivalence principle and the
identity of an inertial or a gravitational pull for an observer in the Einstein
cabin. They value as fore-runners of the self-force and gauge dependency in
general relativity. The approximate nature of Galilei's law of free fall is
explored herein. When stepping into general relativity, we report how the
geodesic free fall into a black hole was the subject of an intense debate again
centred on coordinate choice. Later, we describe how the infalling mass and the
emitted gravitational radiation affect the free fall motion of a body. The
general relativistic self-force might be dealt with to perfectly fit into a
geodesic conception of motion. Then, embracing quantum mechanics, real black
holes are not classical static objects any longer. Free fall has to handle the
Hawking radiation, and leads us to new perspectives on the varying mass of the
evaporating black hole and on the varying energy of the falling mass. Along the
paper, we also estimate our findings for ordinary masses being dropped from a
Galilean or Einsteinian Pisa-like tower with respect to the current state of
the art drawn from precise measurements in ground and space laboratories, and
to the constraints posed by quantum measurements. The appendix describes how
education physics and high impact factor journals discuss the free fall.
Finally, case studies conducted on undergraduate students and teachers are
reviewed
Uniqueness in MHD in divergence form: right nullvectors and well-posedness
Magnetohydrodynamics in divergence form describes a hyperbolic system of
covariant and constraint-free equations. It comprises a linear combination of
an algebraic constraint and Faraday's equations. Here, we study the problem of
well-posedness, and identify a preferred linear combination in this divergence
formulation. The limit of weak magnetic fields shows the slow magnetosonic and
Alfven waves to bifurcate from the contact discontinuity (entropy waves), while
the fast magnetosonic wave is a regular perturbation of the hydrodynamical
sound speed. These results are further reported as a starting point for
characteristic based shock capturing schemes for simulations with
ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy
The Dilution of the Clean Water Act
This Article argues that the zero discharge goal of the Clean Water Act is more than naive rhetoric. To the contrary, it is the Act\u27s raison d\u27ĂȘtre, and it is woven into the fabric of the Act\u27s operative provisions. So understood, the zero discharge goal can and should provide continuing guidance for EPA\u27s implementation of the Act
Scattering Lens Resolves sub-100 nm Structures with Visible Light
The smallest structures that conventional lenses are able to optically
resolve are of the order of 200 nm. We introduce a new type of lens that
exploits multiple scattering of light to generate a scanning nano-sized optical
focus. With an experimental realization of this lens in gallium phosphide we
have succeeded to image gold nanoparticles at 97 nm optical resolution. Our
work is the first lens that provides a resolution in the nanometer regime at
visible wavelengths.Comment: 4 pages, 3 figure
Nonlinear wave equations for relativity
Graviational radiation is described by canonical Yang-Mills wave equations on the curved space-time manifold, together with evolution equations for the metric in the tangent bundle. The initial data problem is described in Yang-Mills scalar and vector potentials, resulting in Lie-constraints in addition to the familiar Gauss-Codacci relations
Entropic force in black hole binaries and its Newtonian limits
We give an exact solution for the static force between two black holes at the
turning points in their binary motion. The results are derived by Gibbs'
principle and the Bekenstein-Hawking entropy applied to the apparent horizon
surfaces in time-symmetric initial data. New power laws are derived for the
entropy jump in mergers, while Newton's law is shown to derive from a new
adiabatic variational principle for the Hilbert action in the presence of
apparent horizon surfaces. In this approach, entropy is strictly monotonic such
that gravity is attractive for all separations including mergers, and the
Bekenstein entropy bound is satisfied also at arbitrarily large separations,
where gravity reduces to Newton's law. The latter is generalized to point
particles in the Newtonian limit by application of Gibbs' principle to
world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.
Gravitational radiation from gamma-ray bursts as observational opportunities for LIGO and VIRGO
Gamma-ray bursts are believed to originate in core-collapse of massive stars.
This produces an active nucleus containing a rapidly rotating Kerr black hole
surrounded by a uniformly magnetized torus represented by two counter-oriented
current rings. We quantify black hole spin-interactions with the torus and
charged particles along open magnetic flux-tubes subtended by the event
horizon. A major output of Egw=4e53 erg is radiated in gravitational waves of
frequency fgw=500 Hz by a quadrupole mass-moment in the torus. Consistent with
GRB-SNe, we find (i) Ts=90s (tens of s, Kouveliotou et al. 1993), (ii)
aspherical SNe of kinetic energy Esn=2e51 erg (2e51 erg in SN1998bw, Hoeflich
et al. 1999) and (iii) GRB-energies Egamma=2e50 erg (3e50erg in Frail et al.
2001). GRB-SNe occur perhaps about once a year within D=100Mpc. Correlating
LIGO/Virgo detectors enables searches for nearby events and their spectral
closure density 6e-9 around 250Hz in the stochastic background radiation in
gravitational waves. At current sensitivity, LIGO-Hanford may place an upper
bound around 150MSolar in GRB030329. Detection of Egw thus provides a method
for identifying Kerr black holes by calorimetry.Comment: to appear in PRD, 49
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